Optimal L(2, 1)-labeling of strong products of cycles [transmitter frequency assignment]

Abstract

The matrix S in Theorem 3 is obtained as S = 3 4 01 01 3 4Since the system equations discussed in [15] require c i = 1(i = 1; 2), the condition given in [15] is not applied. In addition, we can also see that S is not a nonsingular M matrix, so the condition given in [15] does not also hold for the matrices given above. III. CONCLUSIONSA set of criteria have been derived ensuring the global asymptotic stability of delayed cellular neural networks (DCNNs) with more general output functions by introducing ingeniously infinitely real parameters, constructing suitable Lyapunov functionals and applying some analysis techniques, and these criteria are independent of delays and possess infinitely adjustable real parameters w i > 0, 3 ij , 3 ij , 3 ij , 3 ij , ij, ij, ij, ij are any real numbers with 3 ij + 3 ij = 1, ij + ij = 1, 3 ij + 3 ij = 1, ij + j = 1 (i; j = 1; 2; . . . ; n). These are of prime importance and great interest in many application fields and the design of networks. In addition, the methods of this paper may extended to discuss more complicated systems such as Hopfield neural networks(HNNs) and bi-directional associative memory (BAM) networks. ACKNOWLEDGMENTThe author would like to thank the referees and the associate editor for suggesting improvements in presentation.

Optimal L(d,1)-labelings of certain direct products of cycles and Cartesian products of cycles

“…Analogous result is known with respect to 2 1 -numbering of the strong products of cycles [8]. For results with respect to Cartesian products, see [2,7,10,11,14,15].…”

“…Georges and Mauro [1] later presented a generalization of the concept. The topic has since been an object of extensive research [1][2][3][4][7][8][9][10][11][12]14,15].…”

A New Approach to the $L(2,1)$-Labeling of Some Products of Graphs

“…Since , we have thus reduced the bound by . In [12] the -numbers of the strong product of cycles are considered. In [15] and [20], they obtained a general upper bound for the -number of strong products in terms of maximum degrees of the factor graphs (and the product).…”

Improved Bounds on the $L(2,1)$-Number of Direct and Strong Products of Graphs

“…Therefore, we assume and . In [13] and [16], the -numbers of the strong product of cycles are considered. In this section, we obtain a general upper bound for the -number of strong products in terms of maximum degrees of the factor graphs (and the product).…”